No ASND references, but interesting:
Fractals Flowing Online
Advanced Math Could Speed Up
the Internet
From maps to ice crystals to Internet traffic,
fractals can be used to describe seemingly
chaotic patterns and structures.
(ABCNEWS.com)
By Michael J. Martinez
ABCNEWS.com
As you read this sentence, billions of data
packets zip around the Internet, flying
electronically from computer to server and
back again.
All of this traffic can make for some pretty serious traffic jams,
especially at Internet “peerings” — junctions where one network
exchanges traffic with another. Even as networking technology
improves rapidly, it's barely enough to keep up with the
thousands of new users who log on to the Internet every day.
The problem is twofold: most networks are optimized for voice,
not data; and the mathematical nature of data packets — the small
units into which communications over the Internet are broken
down — was, until recently, a mystery. A pair of researchers at
AT&T Labs believe they have uncovered the mathematical keys
to the flow of data packets by analyzing it using fractals —
mathematical patterns used to describe seemingly chaotic
processes such as weather patterns, the way a fire spreads or
how ice crystals form on a window.
The AT&T researchers plan to use fractal patterns to make all
networks — including the Internet — faster and more efficient.
New Mathematical Models
“Once people really started using the
Internet in the late '80s and early '90s,” says
Walter Willinger, a networking researcher at
AT&T Labs in Florham Park, N.J., “they
realized that the old mathematical models
used in the telephone network didn't fit.”
Willinger and fellow researcher Anna
Gilbert used AT&T's PacketScope
technology to study data packets as they
flowed through networks. They observed
that the data formed the same patterns in
whatever time frame they used. A graph of
Internet traffic, showing the number of
packets per unit of time, looks more or less
the same, statistically speaking, whether the
observed time unit is one-hundreth of a second or 100 seconds.
In other words, data packets could be
represented mathematically using fractals.
A fractal is any physical structure or
pattern that looks and acts the same on any
scale. It is statistically comparable (and can
be described mathematically in the same
way) at 2x magnification and at 1,000x
magnification. A map of the British Isles at a
scale of 1 degree latitude, for instance, looks
very different to the human eye than one at
hundreds of degrees. Statistically, however,
they are nearly identical.
Willinger and Gilbert found that, while
each individual Internet session varies
widely in the number and type of data packets sent back and
forth, overall network use can be broken down into common
denominators using fractals.
Put simply: data traffic, no matter how it's looked at,
essentially speaks the same mathematical language.
Spotting Fractal Signatures
Armed with this knowledge, the AT&T researchers are now
looking for ways to optimize servers, personal computers and
networks. Already, they have been able to identify individual
data packets by their fractal signature. That decreases the chance
of corrupted data, since the routers and buffers used in networks
can identify each packet and correctly match them up to the
appropriate user and application.
In addition, Willinger points out, applications designed to use
networks can now be optimized using fractals so that they
function better online.
Gilbert heads a project aimed at more precisely establishing the
fractal nature of data packets.
“Once people understand why we get these patterns,” Gilbert
explains, “we can design better algorithms to deal with the
patterns we see. Instead of completely changing the way packets
are sent across the network, we could change some of the routing
algorithms to make the traffic more efficient.”
Building Better Networks
Eventually, this research could help engineers reconstruct the
networks themselves, using fractal patterns to pinpoint pathways
on the Internet that need to be upgraded.
One looming inefficiency lies in Internet protocols: the way
Internet routers recognize and exchange data.
“Current Internet protocols, like TCP/IP, are outdated,” says
Gilbert. “They were formed before we were really able to use this
knowledge.”
Current protocols don't scale well to new forms of networks,
particularly wireless networks. Dropped data packets are common
in wireless transmissions; with upgraded protocols that take
advantage of fractal traffic flows, dropped or missing data
packets could be pinpointed and reconstructed. “The protocols
used in the wired networks work under the assumption that a
packet is either lost completely or it gets through and is 100
percent correct,” Gilbert says. “We don't have the case where a
packet gets through but is partially corrupted. We have to adapt
the protocols, so that [we can determine when] packets get
through but some are corrupted.”
Another fruitful area could be image-encoding. One of the
challenges of the Internet is rendering large graphics in Web
browsers. But with fractal images, which look the same at any
scale, computers could download a simple formula, then quickly
“build” the image into any size desired. Fractal image encoding
has become a popular field of study at high-tech universities
including the University of California-San Diego, the University
of Waterloo, Canada, and the University of Bath, England.
Practical fractal applications won't leave the lab for at least a
few years. Eventually, however, chaos theory may help reduce
the chaotic nature of the Internet |
